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stat2303_tutorial08

# Assume non trivial case 0 1 1 1 0 0 for 12

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Unformatted text preview: -trivial case 0 , , , , 1. 1 , , 1 0 0 for 1,2, … , 1 0 for 1,2, … , Therefore, all the states communicate with each other, i.e. the Markov chain is irreducible and hence all the states are recurrent. If is even, then for state , 1 0 and hence state is aperiodic. If is odd, then for state , 0 and hence state is aperiodic. Therefore in both cases, the Markov chain is ergodic and the limiting probabilities are obtained by solving 1 for 1,2, … , 1 1 From the first equation, From the third equation, Page 1 of 5 STAT2303/2803 Probability Modelling/Stochastic Models From the second equation, we have 1 and, for Semester 1, 2010­11 1 1 for 1 . Similarly, we ha...
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